I'd like to find such a word instead of saying "greater than 10 but less than 100".
Numbers from 10 to 99 inclusive are often referred to as double figures in the UK.
For example, from yesterday's (British) news:
The death toll during the recent cold snap has hit double figures - as forecasters predicted up to another foot of snow is on the way.
There isn't any context in the question, but if the context is something like
The number of people at the meeting was between 10 and 100
then the phrase to use is in double figures:
The number of people at the meeting was in double figures.
Not an exact answer, but I find it convenient in common parlance to talk about dozens of things. I hear this used more frequently than 10s when describing a rough quantity. For example:
There were dozens of teenagers at the prom.
It tends to describe > 10 but with a fuzzier upper bound--an upper bound small enough that "hundreds" won't do.